Finite Domain Research Articles

A novel low hardware-complexity IQ skew tolerant finite field and time domain hybrid adaptive equalizer for 400G/800G-ZR coherent transmission

A novel low hardware-complexity IQ skew tolerant finite field and time domain hybrid adaptive equalizer for 400G/800G-ZR coherent transmission

Steady state distributions of moving particles in one dimension: with an eye towards axonal transport.

Axonal transport, propelled by motor proteins, plays a crucial role in maintaining the homeostasis of functional and structural components over time. To establish a steady-state distribution of moving particles, what conditions are necessary for axonal transport? This question is pertinent, for instance, to both neurofilaments and mitochondria, which are structural and functional cargoes of axonal transport. In this paper we prove four theorems regarding steady state distributions of moving particles in one dimension on a finite domain. Three of the theorems consider cases where particles approach a uniform distribution at large time. Two consider periodic boundary conditions and one considers reflecting boundary conditions. The other theorem considers reflecting boundary conditions where the velocity is space dependent. If the theoretical results hold in the complex setting of the cell, they would imply that the uniform distribution of neurofilaments observed under healthy conditions appears to require a continuous distribution of neurofilament velocities. Similarly, the spatial distribution of axonal mitochondria may be linked to spatially dependent transport velocities that remain invariant over time.

A characterization of strongly computable finite factorization domains

A characterization of strongly computable finite factorization domains

Non-spinning tops are stable

We consider coupled gravitational and electromagnetic perturbations of a family of five-dimensional Einstein-Maxwell solutions that describes both magnetized black strings and horizonless topological stars. We find that the odd perturbations of this background lead to a master equation with five Fuchsian singularities and compute its quasinormal mode spectrum using three independent methods: Leaver, WKB and numerical integration. Our analysis confirms that odd perturbations always decay in time, while spherically symmetric even perturbations may exhibit for certain ranges of the magnetic fluxes instabilities of Gregory-Laflamme type for black strings and of Gross-Perry-Yaffe type for topological stars. This constitutes evidence that topological stars and black strings are classically stable in a finite domain of their parameter space.

A Semi‐Analytical Method for Simulating Near‐Field Antiplane Wave Propagation in Layered Fluid‐Saturated Porous Media

ABSTRACTA semi‐analytical method for the near‐field antiplane wave propagation analysis in the layered fluid‐saturated porous media (FSPM) is proposed based on the Biot u–U dynamic formulation. The wave propagation equations of the FSPM are decoupled by the variable‐separating method. The thin‐layer element method (TLEM) is applied to discretize the infinite domain and construct the consistent artificial boundary condition. The finite element method (FEM) is adopted for the space discretization of the finite domain and the numerical solution of the dynamic response. The proposed method is validated by the comparison of the numerical results of this method with those in the published references and acquired from the remote artificial boundary. Subsequently, this method is applied to investigate typical near‐field antiplane wave propagation problems in the FSPM. Parametric sensitivity investigations are also executed to explore the impact of mechanical parameters, including permeability coefficients, porosity, and shear modulus of the solid phase, on the dynamic response of the FSPM. The study results confirm the efficacy and efficiency of the proposed method in the near‐field antiplane wave propagation analysis in the FSPM.

Lattice random walk dynamics with stochastic resetting in heterogeneous space

Abstract We examine the diffusive dynamics of a lattice random walk subject to resetting in a one-dimensional spatially heterogeneous environment composed of two media separated by an interface. At random times the walker may reset its position to the interface, but only when in the left medium. In addition the spatial heterogeneity results from having unequal diffusivities and biases in the two media. We construct the Master equation for the dynamics of the walker occupation probability in unbounded space, solve it exactly in terms of generating functions, and analyse the dynamics of the first and second moment. Making use of the closed form solution in the unbounded case, we build the analytic solution of the Master equation in finite and semi-infinite domains. By bounding the space on the right with a reflecting boundary we study the first-passage dynamics to a single fully absorbing target placed in the left medium away from the interface. As reset strongly increases the time to reach the target, we find that the first-passage dynamics enter the motion-limited regime even for relative small resetting probability. We also identify a surprising non-monotonic dependence of the first-passage probability mode as a function of the bias. By deriving an analytic expression for the mean first-passage time, we show when its value is independent of the diffusivity and bias in the left medium, uncovering another example of the so-called mean disorder indifference phenomenon.

Adaptive-coefficient finite difference frequency domain method for time fractional diffusive-viscous wave equation arising in geophysics

The diffusive-viscous wave (DVW) equation is a widely used model to describe frequency dependent attenuation of seismic wave in fluid-saturated porous medium. In this paper taking power law frequency dependent attenuation into account, we first introduce a modified DVW equation (time fractional DVW equation) in which the first order temporal derivative of viscous term is replaced with a fractional order temporal derivative. In consideration of that most of the existing numerical simulations for seismic wave equations are based on time domain methods and truncation with some specific boundary conditions, we incorporate the absorbing boundary condition as complex-frequency-shifted (CFS) perfectly matched layer (PML) into the time fractional DVW equation, and then develop an adaptive-coefficient (AC) finite difference frequency domain (FDFD) method for numerical simulation. The corresponding analytical solution for homogeneous time fractional DVW equation is provided for model validation, and the effectiveness of the developed AC FDFD method is verified by some numerical examples including the homogeneous model and the layered model. Numerical results show that AC FDFD method is more accurate than the traditional 2nd-order FDFD method for numerical modeling of time fractional DVW equation with CFS PML absorbing boundary condition, while requiring similar computational costs.

Boundary controllability for the Korteweg–de Vries–Burgers equation on a finite domain

Boundary controllability for the Korteweg–de Vries–Burgers equation on a finite domain

Thermohaline convection in MHD Casson fluid over an exponentially stretching sheet

Abstract This study investigates the thermohaline convection in MHD Casson fluid over an exponentially stretching sheet. This study has practical significance in industrial processes, materials processing, energy systems, and environmental applications. The governing equations describing the conservation for an electrically conducting fluid flow, thermal and concentration transports are considered based on the principles of mass, momentum, energy and concentration equations. Our first step involves transforming the governing nonlinear partial differential equations into a coupled nonlinear ordinary differential equations with the help of suitable similarity transformations. Second step, infinite domain [0, ∞) of the problem to a finite domain [0, 1] through a coordinate transformations. This specific choice is motivated by the wavelet's significance in the finite domain of [0, 1]. Third step, we effectively solve the resulting coupled nonlinear ordinary differential equations using the numerical Hermite wavelet method (HWM). This approach proves to be a valuable technique for obtaining significant results and insights in our study. Finally, the effect of known physical parameters on velocity, temperature and concentration are analysed through tables and graphs.

Revisiting block deordering in finite-domain state variable planning

Plan deordering removes unnecessary ordering constraints between actions in a plan, facilitating plan execution flexibility and several other tasks, such as plan reuse, modification, and decomposition. Block deordering is a variant of plan deordering that encapsulates coherent actions into blocks to eliminate further ordering constraints from a partial-order plan (POP) and is useful in many applications (e.g., generating macro-actions and improving the overall plan quality). The existing block deordering strategy is formulated in propositional encodings. Finite-domain state variable encodings (e.g., SAS+ representation), in contrast with propositional encodings, can capture the internal structure and the behavior of state variables of a planning instance through concise constructs such as causal graphs (CGs) and domain transition graphs (DTGs). This work redefines the semantics of block deordering terminologies and related plan deordering concepts in finite domain representation (FDR). Our proposed semantics also resolves some limitations of the existing block semantics and further enhance plan flexibility. In addition, this work exploits block deordering to eliminate redundant actions from a POP. A comparative analysis is also performed on block deordering with various deordering/reordering techniques using explanation-based order generalization (EOG) and MaxSAT. Our experiments on the benchmark problems from International Planning Competitions (IPC) show that our FDR formalism of block deordering significantly improves the plan execution flexibility while maintaining good coverage and execution time.

Stability of KdV equation on a network with bounded and unbounded lengths

In this work, we studied the exponential stability of the nonlinear KdV equation posed on a finite star shaped network with finite number of branches. On each branch of the network we define a KdV equation posed on a finite domain [[EQUATION]] or the half-line [[EQUATION]]. We start by proving well-posedness and some regularity results. Then, we state the exponential stability of the linear KdV equation by acting with a damping term on some branches. The main idea is to prove a suitable observability inequality. In the nonlinear case, we obtain two kinds of results: The first result holds for small amplitude solutions, and is proved using a perturbation argument from the linear case but without acting on all edges. The second result is a semiglobal stability result, and it is obtained by proving an observability inequality directly for the nonlinear system, but we need to act with damping terms on all the branches. In this case, we are able to prove the stabilization in weighted spaces.

De Sitter State in Heterotic String Theory

AbstractRecent no‐go theorems have ruled out four‐dimensional classical de Sitter vacua in heterotic string theory. On the other hand, the absence of a well‐defined Wilsonian effective action and other related phenomena also appear to rule out such time‐dependent vacua with de Sitter isometries, even in the presence of quantum corrections. In this note, the authors argued that a four‐dimensional de Sitter space can still exist in heterotic string theory as a Glauber–Sudarshan state, i.e., as an excited state, over a supersymmetric Minkowski background, albeit within a finite temporal domain. Borel resummation and resurgence play a crucial role in constructing such a state in the Hilbert space of heterotic theory governed entirely by the IR degrees of freedom.

The Blockage Effect on Resistance Coefficients Estimation for AUVs with Different Configurations in the Towing Tank

When a resistance test of an underwater vehicle model is conducted in a towing tank, the blockage effect will inevitably occur, particularly since the experimental model is relatively large. This paper investigates the estimation of resistance coefficients for an Axisymmetrical Rotary Body Underwater Vehicle (ARBUV) and a Blended Wing Body Underwater Vehicle (BWBUV). The Computational Fluid Dynamics (CFD) method is employed to predict the resistance of Autonomous Underwater Vehicles (AUVs). In order to quantify the blockage effect on the resistance coefficients of AUVs with different configurations, the resistance coefficients of AUVs are calculated in the infinite domain and finite domain under various blockage ratios. Through analysis of the resistance results, velocity distribution, and pressure distribution, the action law of the blockage effect is provided. It indicates that blockage effects have a greater influence on the pressure resistance for ARBUV. Surprisingly, the resistance coefficients of BWBUV are less affected, though it is closer to the sidewalls. It suggests that the blockage ratio of ARBUV and BWBUV should be separately smaller than 0.375% and 2.5% in the towing tank test. The towing tank experiments satisfy the blocking ratio with a Reynolds number greater than 107, which saturates the blocking effect and further reduces the effect on the drag coefficient.

A p-Multigrid Hybrid-Spectral Model for Nonlinear Water Waves

AbstractTo improve both scale and fidelity of numerical water wave simulations to study the evolution of wave fields within offshore engineering, it is of key practical interest to achieve high numerical efficiency. We propose a p-multigrid accelerated time-domain scheme for efficient and $${\mathcal {O}}(n \log n)$$ O ( n log n ) -scalable solution of a hybrid-spectral model for the simulation of highly nonlinear and highly dispersive water waves, the accurate calculation of wave kinematics and taking into account varying water depth. To achieve low numerical dispersive and dissipate errors, a high-order hybrid-spectral collocation scheme is implemented to solve the fully nonlinear potential flow (FNPF) equations, and utilizing a p-multigrid iterative solver scheme for solving the Laplace problem. Hereby, the numerical scheme combines the high accuracy of spectral methods, high efficiency of the fast Fourier transform (FFT) algorithm, and multigrid methods. Numerical analysis is performed to evaluate the performance and confirm the spectral accuracy of the scheme. Numerical experiments are considered for steady nonlinear wave propagation. A Fourier-continuation technique is used to extend the scheme from a periodic domain setup to perform benchmarks in a finite domain setup for numerical wave tanks utilizing conventional techniques for wave generation and absorption, and with results in excellent agreement with experimental measurements.

Analysis of conductive filament heat transfer in TiO2-based RRAM device

Abstract Resistive random access memory (RRAM) has developed into a new type of non-volatile memory that has attracted much attention for its high density and low power; TiO2 has been studied to make RRAM because of its high conductivity. Based on the COMSOL Multiphysics finite element method and domain decomposition method, an electrically-thermally coupled model of TiO2-based RRAM with oxygen vacancy (Vo) conduction mechanism is constructed, the formation and cutting process of RESET and SET conductive filament (CF) under different voltages is simulated. Moreover, the characteristics of the internal temperature distribution of the CF are explored. The results show that the RESET process is more sensitive to heat changes, the transverse direction thermal value of the CF is more obvious than the longitudinal direction, and the rate of change is faster. Additionally, the electric field induces the migration of the Vo in filament, which affects the enthalpy change of the device’s heat transfer and resistive properties. This is an important reference for a deeper understanding of the switching behavior of RRAM devices and the control mechanisms for thermal studies.

Finite domain solution of a hydraulic fracture in a permeable rock

In this work, we present a domain-based algorithm to simulate the propagation of a plane-strain hydraulic fracture in a zero-toughness permeable elastic medium. The algorithm utilizes a domain-based method to solve the elasticity equations and integrates a multi-scale tip asymptote, which is particular to hydraulic fractures, into this framework. This integration is key to accurately model the energy dissipation and the fluid leak-off in the fracture tip region. The algorithm combines a 2D finite volume method (FVM) for solving the elasticity equation with a 1D FVM for solving the nonlinear lubrication equation. Incorporating the far-field asymptotics and using a moving-mesh scheme reduces the computational burden while improving the accuracy of the scheme. The paper concludes with an analysis of the numerical results. This study demonstrates the potential of this domain-based approach for modeling hydraulic fractures in poroelastic media.

Energy-saving mechanism of series–parallel hybrid transmissions — A dynamic programming method based on matrix operations

The economic evaluation of hybrid transmission is a complicated numerical calculation problem in the finite time domain. Currently, employing traditional dynamic programming methods to evaluate a single design scheme consumes a lot of time, making it arduous to effectively compare performance disparities across various design schemes. This paper introduces a dynamic programming method based on matrix operations, enabling the determination of maximum energy-saving potential in hybrid transmission while reducing the evaluation time for a single design scheme from hours to less than 10 s. It unifies the design variables, constraints, and optimization objectives for multi-gear and multi-mode series–parallel hybrid transmissions (MGMM-SPHTs) during economic evaluation. By solving the performance of tens of thousands of design schemes, it is found that increasing the number of engine direct drive gears from 1 to 2 enhances the economy and power performance of series–parallel hybrid transmissions. For the optimal design scheme of Type-B vehicles, this enhancement results in a 1.712% increase in energy-saving efficiency and a 30.5% increment in power performance. Furthermore, this paper elucidates the adaptive relationship between MGMM-SPHTs and different vehicle types, revealing the energy-saving mechanisms under varied design schemes. This paper holds the promise of offering theoretical underpinnings and methodological instruments for selecting technical routes and optimizing design parameters for MGMM-SPHTs.

Distributed adaptive tracking consensus control for a class of heterogeneous nonlinear multi-agent systems

The proposed approach differs from existing works in that it models the constraints of each follower as a nonlinear strict feedback system, rather than relying on a desired reference trajectory for accessible subsystems. To address the limitations caused by uncertain terms in systems, radial basis functions neural networks are utilized to compensate for these unknown nonlinear terms. This leads to a novel distributed adaptive consensus tracking control protocol for high-order nonlinear heterogeneous multi-agent systems, based on the backstepping technique. By introducing a non-zero parameter in the traditional radial basis functions neural network, a new universal approximation is constructed, which overcomes the limitation of the approximation’s finite domain. Additionally, the approximation precision can be adjusted online using provided laws, and the dimension explosion of virtual and real control gains can be avoided through the use of the designed control approach. Simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

Full counting statistics of 1d short range Riesz gases in confinement

We investigate the full counting statistics of a harmonically confined 1d short range Riesz gas consisting of N particles in equilibrium at finite temperature. The particles interact with each other through a repulsive power-law interaction with an exponent k > 1 which includes the Calogero–Moser model for k = 2. We examine the probability distribution of the number of particles in a finite domain [−W,W] called number distribution, denoted by N(W,N) . We analyze the probability distribution of N(W,N) and show that it exhibits a large deviation form for large N characterized by a speed N3k+2k+2 and by a large deviation function (LDF) of the fraction c=N(W,N)/N of the particles inside the domain and W. We show that the density profiles that create the large deviations display interesting shape transitions as one varies c and W. This is manifested by a third-order phase transition exhibited by the LDF that has discontinuous third derivatives. Monte–Carlo simulations based on Metropolis–Hashtings (MH) algorithm show good agreement with our analytical expressions for the corresponding density profiles. We find that the typical fluctuations of N(W,N) , obtained from our field theoretic calculations are Gaussian distributed with a variance that scales as Nνk , with νk=(2−k)/(2+k) . We also present some numerical findings on the mean and the variance. Furthermore, we adapt our formalism to study the index distribution (where the domain is semi-infinite (−∞,W]) , linear statistics (the variance), thermodynamic pressure and bulk modulus.

A fast numerical algorithm for finding all real solutions to a system of N nonlinear equations in a finite domain

AbstractA highly recurrent traditional bottleneck in applied mathematics, for which the most popular codes (Mathematica, Matlab, and Python as examples) do not offer a solution, is to find all the real solutions of a system of n nonlinear equations in a certain finite domain of the n-dimensional space of variables. We present two similar algorithms of minimum length and computational weight to solve this problem, in which one resembles a graphical tool of edge detection in an image extended to n dimensions. To do this, we discretize the n-dimensional space sector in which the solutions are sought. Once the discretized hypersurfaces (edges) defined by each nonlinear equation of the n-dimensional system have been identified in a single, simultaneous step, the coincidence of the hypersurfaces in each n-dimensional tile or cell containing at least one solution marks the approximate locations of all the hyperpoints that constitute the solutions. This makes the final Newton-Raphson step rapidly convergent to all the existent solutions in the predefined space sector with the desired degree of accuracy.